Question

If the distance halfway around Mercury is 4,761 mi., then what is the length of the diameter of the planet to the nearest mile?(1 point)Responses3,031 mi.3,031 mi.4,761 mi.4,761 mi.1,515 mi.1,515 mi.14,957 mi.14,957 mi.

Answer 1

To find the diameter of Mercury given that the distance halfway around the planet (which is half the circumference) is 4,761 miles, we can use the formula for the circumference of a circle, which is:

\[
C = \pi d
\]

where \( C \) is the circumference and \( d \) is the diameter. Since halfway around Mercury is 4,761 miles, we can express the full circumference as:

\[
C = 2 \times 4,761 = 9,522 \text{ miles}
\]

Now we can use the circumference to find the diameter:

\[
9,522 = \pi d
\]

To solve for \( d \), we can rearrange the equation:

\[
d = \frac{9,522}{\pi}
\]

Using the approximate value of \( \pi \) as 3.14:

\[
d \approx \frac{9,522}{3.14} \approx 3,032 \text{ miles}
\]

Rounding to the nearest mile gives us a diameter of approximately 3,031 miles, which matches one of the response options.

Thus, the answer is:

**3,031 mi.**